Tuesday, November 19, 2013

The Fictional and the Merely Possible

"To be or not to be, that is the question." Or at least that is one question. Another is whether Hamlet, that very individual, might have been actual.

It is a mistake to conflate the fictional and the merely possible. Hamlet, for example, is a fictional individual, the central character and eponym of the Shakespearean play. Being fictional, he does not actually exist. But one might be tempted to suppose that while there is no man Hamlet in actuality, there could have been, that Hamlet is a possible individual. But far from being possible, Hamlet is impossible. Or so I shall argue.

D2. x is incomplete =df there is a property P such that x is indeterminate with respect to P, i.e., it is not the case that x instantiates P and it is not the case that x does not instantiate P.

The Main Argument

1. Hamlet is an incomplete object. He has all and only the properties ascribed to him in the play that bears his name. It is neither the case that he eats his eggs with hot sauce nor that he doesn't.

2. Necessarily, for any x, if x is an incomplete object, then x does not exist.

Therefore

3. Necessarily, Hamlet does not exist. (from 1, 2)

Therefore

4. Hamlet is an impossible object. (from 3, D1)

The reasoning is correct and premise (1) is surely true. If you are inclined to reject (2), claiming that it does not hold for quantum phenomena, I will simply sidestep that whole can of worms by inserting 'macroscopic' or 'mesoscopic' or some other suitable qualifier between 'an' and 'incomplete.'

Note that Hamlet is impossible even if the properties he is ascribed in the play are members of a logically consistent set. One could say, with a whiff of paradox, that Hamlet is impossible despite the fact that his properties are compossible. His impossibility follows from his incompleteness. What this shows is that not every impossible object harbors internal contradiction. So there there are at least two types of impossibilia, those whose impossibility derives from inconsistency and those whose impossibility derives from incompleteness. To be admitted to the elite corps of the actual, one must satisfy both LNC and LEM. That the impossible needn't be internally contradictory is an insight I owe to Daniel Novotny who kindly sent me a free copy of his excellent book on the scholasticism of the Baroque era entitled, Ens Rationis from Suarez to Caramuel (Fordham 2013). I am indebted in particular to his discussion on p. 108.

Objection: "Hamlet is possible; it is just that his actualization would have to consist in his completion. Surely God could actualize Shakespeare's Hamlet (the prince, not the play) by appropriately supplementing his property set."

Reply: Suppose God were to try to actualize Hamlet, the very same individual encountered in the play. To do so, God would have to supplement Hamlet's property set, bringing it to completeness. For only that which is wholly determinate can exist in (macroscopic) actuality. But there is more than one way to effect this supplementation. For example, if the fictional Hamlet is indeterminate with respect to whether or not he takes his eggs with hot sauce, an actual Hamlet cannot be. He either eats egggs or he doesn't, and he either takes them with hot sauce or he doesn't.

Let AH1 be hot-sauce Hamlet and AH2 non-hot-sauce Hamlet. Both are complete. Let FH be the incomplete fictional individual in the play.

We may now argue as follows.

If God brings about the actuality of both AH1 and AH2, then, since they are numerically distinct, neither of them can be identical to FH. But God must actualize one or the other if FH is to become actual. If God actualizes one but not the other, then it is possible that he actualize the other but not the the one. But then the actualization of either is contingent. Thus if God actualizes FH as AH1, then, since he could just as well have actualized AH2 as FH, the identity of FH with AH1 is contingent. But identity cannot be contingent: if x = y, then necessarily x = y. Therefore, God can actualize neither and fictional Hamlet is impossibly actual, i.e., impossible.

Here is a third consideration. It seems to be part of the very sense of the phrase 'fictional individual' that such individuals be, well, fictional, that is, irreal or unreal. Now the real includes not only the actual and the necessary, but that which is really possible albeit unactual. Thus real possibilities cannot be made up by minds and so cannot be fictional. Therefore Hamlet, as a fictional being, is not a possible being.

According to Novotny, "Suarez and other Baroque scholastic authors seem to assume without question that consistent fictions, such as Hamlet, might become real beings. This implies that Hamlet is a possible being and that therefore he is a real being. [. . .] For several reasons I do not think that a consistent fiction as such is a real possible being." (108)

I agree, and the arguments above are my way of fleshing out Novotny's misgivings.

Addendum (21 November)

The original main argument above is invalid as a commenter points out. Here is

The Main Argument Repaired

0. Necessarily, for every x, if x is a fictum of a finite mind, then x is incomplete.

0*. Necessarily, Hamlet is a fictum of a finite mind, Shakespeare's. (That very fictional individual could not have been the fictum of any other mind.)

Therefore

1. Necessarily, Hamlet is an incomplete object. He has all and only the properties ascribed to him in the play that bears his name. It is neither the case that he eats his eggs with hot sauce nor that he doesn't. (from 0, 0*)

2. Necessarily, for any x, if x is an incomplete object, then x does not exist.

Comments

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"Hamlet is an incomplete object. He has all and only the properties ascribed to him in the play that bears his name. It is neither the case that he eats his eggs with hot sauce or that he doesn't. "

I don't follow this at all. I don't agree with the second sentence "He has all and only ….". Of course Shakespeare said that there was a person called ‘Hamlet’ who had certain properties (e.g. he said that Hamlet was a prince of Denmark. It doesn’t follow that there is someone who has or had such a property. For example, legend says that there was a horse called ‘Pegasus’ that flew. It doesn’t follow that there are or were flying horses.

And why does it follow that because someone fails us to provide us with certain information about something, that the information neither applies nor fails to apply? For example, I have never told you the colour of the front door of our house. It doesn’t follow that the door doesn’t have a colour.

Good old London Ed, true to form, balks or rather baulks right at the git-go, rejecting (1)which I claimed is "surely true." Maybe I shouldn't have brought Shirley into it. In any case, I need a separate post to respond.

You are quite right about this. You have shown that an argument pattern in modal propositional logic is invalid. But my inference is of a different pattern, and involves quantification.

Can you provide a counterexample to it?

In any case, I am comfortable with strengthening (1) to 'Necessarily, Hamlet is an incomplete object.'

You say that someone could give a complete description of Hamlet. Well, God could, but not any finite novelist or story-teller, not even the Bard himself. For there are infinitely many properties, perhaps even continuum-many. You would have to specify all of Hamlet's relational properties and all their entailments for starters. When he gave his soliloquy, how far was he from the moon, and what were the exact contents of his GI tract, etc. ad infinitum?

The incompleteness of fictional objects is the mirror image of the finitude of the human mind.

Okay. So, more technically, your argument has the following structure:

1. Fx
2. [] (x)(Fx -> Gx)
3. [] Gx

Right? But, this is still invalid. Consider this argument:

4. I own a dog.
5. Necessarily, for any x, if x owns a dog then x owns a mammal.
6. So, necessarily, I own a mammal.

(4) and (5) are true, yet, (6) is false. So, the argument is invalid. We could fix the structure by making the first premise necessary. But, that would make it unsound.

Now, since this is the same structure of your argument, it, too, is invalid, unless we fix the first premise, which you said you're willing to do. But, I then claimed that the new premises was false; for someone could give a complete description of Hamlet. You respond by saying that only God could. Well, that's good enough, right? If God could do it, then it's true that someone could do it and, thus, it's not an impossible object.

But, I also think it's false that only God could do it. We could suppose there's a possible world in which the Bard is writing on a super-duper computer and, recognizing that he could never type out a complete description of Hamlet, he asks the computer to perform a supertask to do it. Now, of course, this depends on the possibility of supertasks, which you may deny. But, I don't. So, here we may be at an impasse.

I think, now, that in order for your argument to work you need (0*) to work with per se necessity. However, I suspect that it's only working with per accidens necessity. That is, it seems that it might only be an accident of history that Hamlet is the product of Shakespeare. As I said in my previous comment, it seems like there's a possible world in which Shakespeare or somebody else writes Hamlet on a computer that's capable of performing a supertask that gives a complete description of Hamlet.

So, if all this is correct then the argument is still invalid since it equivocates on the word "necessarily." In (0*), it means per accidens necessity, but in the conclusion it means per se necessity.

Arizona Bill:
No, we haven´t, if you mean the Analytic theology meeting, I wasn´t there ...
To your question: I would say that it is very hard question. It reminds me of (I think) similar problem: we have some song. Was this song really invented, composed, or was it in fact only "discovered"?

Anyway, I am prone more to agree with reply 2. At least from the moment Hamlet was made up, he became mind-independent in a sense ...

>>That is, it seems that it might only be an accident of history that Hamlet is the product of Shakespeare.<<

I'm afraid that makes no sense to me. There is no Hamlet apart from Shakespeare's creative acts. That very character could not have been originated by anyone else. (This is of course consistent with there being Hamlet-like characters in other plays and novels by other writers.)

By my opinion, it is necessary to distinguish between objects and descriptions of objects. Hamlet is an object, Shakespeare play is a description of object.

So, according to this view, your sentence "Hamlet is an incomplete object" is wrong, because what is incomplete is description of Hamlet.

It is impossible to guess anything about existence of objects from incompleteness of theirs descriptions.

I think you should also take into account that every description of each physically existent object is incomplete. It is even impossible to give complete description of any physical objects (at least if we go on particle level).

So nothing existed ?

How do you know Richard III really existed ? You know about him only from books. And, according to your line of arguments, he is also "incomplete".

I apologize that I wrote too much. Thanks for the answers, now I undestand you better.

But I still have some problems: it seems to me, that you distinguish between possible, but unactual, and fictional.
I undestand, that fictional is not possible - but there is a practical question: how do you know, what is and what is not "really" possible ? It is not actual, so you cannot use sense data. In both of the cases you have only descriptions, and they both are necessarily incomplete. From practical point of view, it is undistiguishable (if we leave aside probability), difference is only "ontological".

So, as it seems to me, that if we accept your conclusions, than every thought or written sentence in the form of "X is possible" must be a contradiction, because we were not able to include all the properties of X. So X is incomplete, according to you also impossible, and therefore the sentence is contradictory.

Maybe it is nonsense, but I would like to mention one idea:
I think for universals is also true, that "there is a property P such that x is indeterminate with respect to P".
If object with properties, ascribed to Hamlet, could be (hypothetically) actualized in many slightly different instances, than could it not be so that Shakespeare's hero is, in fact, a universal ?
If it is acceptable, than is it correct to say about some universal X that "X is possible" ? If yes, than why it could be wrong in principle to says just the same about Hamlet ?

About your third consideration: "It seems to be part of the very sense of the phrase 'fictional individual' that such individuals be, well, fictional, that is, irreal or unreal. ..."
"Fictional individual" is not the property of Hamlet, ascribed to him in the play. It is the fact of history.
So, I think, it is not the fact of the discourse, it is the fact of the metadiscourse. As such, it could not be used in proofs of possibility of Hamlet's actual existence.
I think "third consideration" is similar like to argue that some invented machine cannot be constructed, because invention is mental creation and thus immaterial.